The Beer Diet

I know it's been pretty quiet over here this week.  The semester is winding down (a week of classes left), and that means that things have been kicked up into another gear.  We've got four or five ideas bouncing around at the moment, so hopefully we'll get some up soon.  Today I'd like to talk about the beer diet.  A while back, there was a rumor going around that if you drank ice cold beer your body would burn more calories heating the beer than the beer contained.  It turns out that this false, and I think the claim relied on a lack of knowledge that the American food Calorie is actually one thousand calories (note the difference in capitalization).  Let's prove this to ourselves.

Let us consider 12 fluid oz of beer.  To any good approximation we can treat this as 12 oz of water.  Let us assume that the beer starts at 0C and our body raises it to body temperature, 37C.  This takes energy Q given by
\[Q=mc\Delta T\]
Where m is the mass of the beer, c the specific heat of water, and the last term the change in temperature.  We convert out of the archaic units (thanks google!) to get 12 oz = .35 liters.  The density of water is 1000kg/m^3, which is 1kg/liter.  This gives us the mass of the beer as .35 kg.  The specific heat of water is 1 kcal/kg*C (note: kcal = kilocalorie = 1 Calorie, i.e. 1000 calories), so the energy it takes to change the temperature of our beer is
\[Q=(.35kg)(1kcal/kg*C)(37C-0C)\]
\[Q=13kcal\]

If memory serves, some beer company recently had ads toting how their light beer was 'under 100 Calories'.  So, I imagine 100 kcal is a fairly good lower bound on the calories in a 12 oz beer.  So you can't lose weight just by drinking beer.  Sad, isn't it?  Finally, we can see that if we didn't understand the distinction between Calorie and calorie, we might think that, since it took 1300 calories to heat up the beer, and beer only contains 100 Calories, this would be a great way to lose weight!

I leave it as a question for you, dear readers, as to how much ice water you'd have to drink to have an effective ice water diet.  If it does become the next fad diet, you heard about it here first!